Abstract
We prove existence and uniqueness of weak solutions for the minimizing Total Variation flow with initial data in L 1 under Neumann boundary conditions. We prove that the H N−1 measure of the boundaries of level sets of the solution decreases with time, as one would expect. We also prove that local maxima (minima) strictly decrease (increase) their level with time. We shall also consider the Dirichlet problem which presents some particular difficulties for general initial data in L 1.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Comptes Rendus de l'Academie des Sciences Series I Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
